The diameter of the inscribed circle in a regular hexagon is 4√3 inches long. What is the perimeter of this regular hexagon?

12√3 inches or 20.785 inches.

Step-by-step explanation:

A regular hexagon can be defined as a polygon with 6 sides.

The formula for the perimeter of a regular hexagon =

6 × the length of the sides of the hexagon.

From the above question, we are told that there is an inscribed circle I'm the hexagon with a diameter of 4√3 inches long

Step 1

Find the radius of the circle

Radius of the circle = 4√3/2 = 2√3 inches

Step 2

The radius of the inscribed circle = Length of one of the sides of a regular hexagon.

Hence, the perimeter of the regular hexagon = 6 × 2√3

= 12√3 inches

= 20.784609691 inches.

Approximately 20.785 inches

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